Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
258 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 18. C5×#689 | C4 | semidirect |
| 19. #87776 | C4 | semidirect |
| 69. #689 | AGL(1,𝔽5) | semidirect |
| 106. C52 | #441 | semidirect |
| 158. C5 | #65739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#1044 | 2 |
| #11717355 | 2 |
| #11717062 | 2 |
| #11716877 | 2 |
| #11716771 | 2 |
| #11716768 | 2 |
| #11716764 | 2 |
| #65739 | 5 |